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## Chemical equilibrium
In a chemical process,
## Additional recommended knowledge
## IntroductionIn a chemical reaction, when reactants are mixed together in a reaction vessel (and heated if needed), the whole of reactants do not get converted into the products. After some time (which may be shorter than millionths of a second or longer than the age of the universe), there will come a point when a fixed amount of reactants will exist in harmony with a fixed amount of products, the amounts of neither changing anymore. This is called chemical equilibrium. The concept of chemical equilibrium was developed after Berthollet (1803) found that some chemical reactions are reversible. For any reaction such as to be at equilibrium the rates of the forward and backward (reverse) reactions have to be equal. In this chemical equation with harpoon arrows pointing both ways to indicate equilibrium, A and B are reactant chemical species, S and T are product species, and α, β, σ, and τ are the stoichiometric coefficients of the respective reactants and products. The equilibrium position of a reaction is said to lie far to the right if, at equilibrium, nearly all the reactants are used up and far to the left if hardly any product is formed from the reactants. Guldberg and Waage (1865), building on Berthollet’s ideas, proposed the law of mass action: where A, B, S and T are active masses and k and the ratio of the rate constants is also a constant, now known as an equilibrium constant. By convention the products form the numerator.
Unfortunately, the law of mass action is valid only for concerted one-step reactions that proceed through a single transition state and is Despite the failure of this derivation, the equilibrium constant for a reaction is indeed a constant, independent of the activities of the various species involved, though it does depend on temperature as observed by the van 't Hoff equation. Adding a catalyst will affect both the forward reaction and the reverse reaction in the same way and will not have an effect on the equilibrium constant. The catalyst will speed up both reactions thereby increasing the speed at which equilibrium is reached. Although the macroscopic equilibrium concentrations are constant in time reactions do occur at the molecular level. For example, in the case of ethanoic acid dissolved in water and forming ethanoate and hydronium ions, - CH
_{3}CO_{2}H + H_{2}O ⇌ CH_{3}CO_{2}^{−}+ H_{3}O^{+}
a proton may hop from one molecule of ethanoic acid on to a water molecule and then on to an ethanoate ion to form another molecule of ethanoic acid and leaving the number of ethanoic acid molecules unchanged. This is an example of dynamic equilibrium. Equilibriums, like the rest of thermodynamics, are statistical phenomena, averages of microscopic behaviour. Le Chatelier's principle (1884) is a useful principle that gives a qualitative idea of an equilibrium system's response to changes in reaction conditions. If mineral acid is added to the ethanoic acid mixture, increasing the concentration of hydronium ion, the amount of dissociation must decrease as the reaction is driven to the left in accordance with this principle. This can also be deduced from the equilibrium constant expression for the reaction: if {H A quantitative version is given by the reaction quotient. J.W. Gibbs suggested in 1873 that equilibrium is attained when the Gibbs energy of the system is at its minimum value (assuming the reaction is carried out under constant pressure). What this means is, the derivative of the Gibbs energy with respect to reaction coordinate (a measure of the extent of reaction that has occurred, ranging from zero for all reactants to a maximum for all products) vanishes, signalling a stationary point. This derivative is usually called, for certain technical reasons, the Gibbs energy change. where R is the universal gas constant and T the temperature. When the reactants are dissolved in a medium of high ionic strength the quotient of activity coefficients may be taken to be constant. In that case the where [A] is the concentration of A, etc., is independent of the analytical concentration of the reactants. For this reason, equilibrium constants for solutions are usually determined in media of high ionic strength. K ## ThermodynamicsThe relationship between the Gibbs energy and the equilibrium constant can be found by considering chemical potentials. The thermodynamic condition for chemical equilibrium is - At constant pressure ΔG=0 (ΔG is the change Gibbs free energy for the reaction)
- At constant volume ΔA=0 (ΔA is the change in Helmholtz free energy for the reaction)
In this article only the constant pressure case is considered. The constant volume case is important in geochemistry and atmospheric chemistry where pressure variations are significant. Note that if reactants and products were in standard state (completely pure) then there would be no reversibility and no equilibrium. The mixing of the products and reactants contributes a large entropy (known as entropy of mixing) to states containing equal mixture of products and reactants. The combination of the standard Gibbs energy change and the Gibbs energy of mixing determines the equilibrium state. In general an equilibrium system is defined by writing an equilibrium equation for the reaction To meet the thermodynamic condition for equilibrium the Gibbs energy must be stationary, meaning that the derivative of G with respect to reaction coordinate (ΔG) must be zero. It can be shown that ΔG is in fact equal to the difference between the chemical potentials of the products and those of the reactants. Therefore, the sum of the Gibbs energies of the reactants must be the equal to the sum of the Gibbs energies of the products. where μ is in this case a partial molar Gibbs energy, a chemical potential. The chemical potential of a reagent A is a function of the activity, {A} of that reagent. Substituting expressions like this into the Gibbs energy equation: which at constant pressure and temperature becomes: results in: By substituting the chemical potentials: the relationship becomes: At equilibrium and therefore leading to: ΔG ## Treatment of activityThe expression for the equilibrium constant can be re-written as the product of a concentration quotient, [A] is the concentration of reagent A etc. It is possible in principle to obtain values of the activity coefficients, γ. For solutions equations such as the Debye-Hückel equation or extensions such as Davies equation For reactions in the gas phase partial pressure is used in place of concentration and fugacity coefficient in place of activity coefficient. In the real world, for example when making ammonia industrially, fugacity coefficients must be taken into account. Fugacity, so the general expression defining an equilibrium constant is valid for both solution and gas phases. ## Justification for the use of concentration quotientsIn aqueous solution, equilibrium constants are usually determined in the presence of an "inert" electrolyte such as sodium nitrate NaNO where However, To use a published value of an equilibrium constant in conditions of ionic strength different from the conditions used in its determination, the value should be adjusted ## Metastable mixturesA mixture may be appear to have no tendency to change, though it is not at equilibrium. For example, a mixture of SO - 2SO
_{2}+ O_{2}2SO_{3}
The barrier can be overcome when a catalyst is also present in the mixture as in the Contact process, but the catalyst does not affect the equilibrium concentrations. Likewise, the formation of bicarbonate from carbon dioxide and water is very slow under normal conditions - CO
_{2}+ 2H_{2}O HCO_{3}^{-}+H_{3}O^{+}
but almost instantaneous in the presence of the catalytic enzyme carbonic anhydrase. ## Pure compounds in equilibriaWhen pure substances (liquids or solids) are involved in equilibria they do not appear in the equilibrium equation Applying the general formula for an equilibrium constant to the specific case of ethanoic acid one obtains It may be assumed that the concentration of water is constant. This assumption will be valid for all but very concentrated solutions. The equilibrium constant expression is therefore usually written as where now
a constant factor is incorporated into the equilibrium constant. A particular case is the self-ionization of water itself The self-ionization constant of water is defined as
It is perfectly legitimate to write [H The concentrations of H Solids also do not appear in the equilibrium equation. An example is the Boudouard reaction for which the equation (without solid carbon) is written as: ## Multiple equilibriaConsider the case of a dibasic acid H
Note that these constants are dissociation constants because the products on the right hand side of the equilibrium expression are dissociation products. In many systems it is preferable to use association constants. β ## Effect of temperature change on an equilibrium constantThe effect of changing temperature on an equilibrium constant is given by the van 't Hoff equation Thus, for exothermic reactions, (ΔH is negative) At first sight this appears to offer a means of obtaining the standard molar enthalpy of the reaction by studying the variation of ## Types of equilibrium and some applications- In the gas phase. Rocket engines
^{[13]} - The industrial synthesis such as ammonia in the Haber-Bosch process (depicted right) takes place through a succession of equilibrium steps including adsorbtion processes.
- atmospheric chemistry.
- Seawater and other natural waters. Chemical oceanography.
- Distribution between two phases.
- LogD-Distribution coefficient Important for pharmaceuticals where lipophilicity is a significant property of a drug.
- Liquid-liquid extraction, Ion exchange, Chromatography.
- Solubility product.
- Uptake and release of oxygen by haemoglobin in blood
- Acid/base equilibria. Acid dissociation constant, hydrolysis, buffer solutions, indicators, acid-base homeostasis
- Metal-ligand complexation. sequestering agents, chelation therapy, MRI contrast reagents, Schlenk equilibrium
- Adduct formation. Host-guest chemistry, supramolecular chemistry, molecular recognition, dinitrogen tetroxide
- In certain oscillating reactions the approach to equilibrium is not asymptotically but in the form of a damped oscillation
^{[11]}. - The related Nernst equation in electrochemistry gives the difference in electrode potential as a function of redox concentrations.
- When molecules on each side of the equilibrium are able to further react irreversibly in secondary reactions the final product ratio is determined according to the Curtin-Hammett principle.
In these applications terms such as stability constant, formation constant, binding constant, affinity constant, association/dissociation constant are used. In biochemistry it is common to give units for binding constants, which serve to define the concentration units used when the constant’s value was determined. ## Composition of an equilibrium mixtureWhen the only equilibrium is that of the formation of a 1:1 adduct as the composition of a mixture, there are any number of ways that the composition of a mixture can be calculated. For example, see ICE table for a traditional method of calculating the pH of a solution of a weak acid. There are three approaches to the general calculation of the composition of a mixture at equilibrium. - The most basic approach is to manipulate the various equilibrium constants until the desired concentrations are expressed in terms of measured equilibrium constants (equivalent to measuring chemical potentials) and initial conditions.
- Minimize the Gibbs energy of the system.
^{[14]} - Satisfy the equation of mass balance. The equations of mass balance are simply statements that the total concentration of each reactant must be constant by the law of conservation of mass.
## Solving the equations of mass-balanceIn general the calculations are rather complicated. For instance, in the case of a dibasic acid, H With T When the equilibrium constants are known and the total concentrations are specified there are two equations in two unknown "free concentrations" [A] and [H]. This follows from the fact that [HA]= β so the concentrations of the "complexes" are calculated from the free concentrations and the equilibrium constants. General expressions applicable to all systems with two reagents, A and B would be It is easy to see how this can be extended to three or more reagents. ## Composition for polybasic acids as a function of pHThe composition of solutions containing reactants A and H is easy to calculate as a function of p[H]. When [H] is known the free concentration [A] is calculated from the mass-balance equation in A. Here is an example of the results that can be obtained.
This diagram, for the hydrolysis of the aluminum Lewis acid Al ## Solution equilibria with precipitationThe diagram above illustrates the point that a precipitate may be formed which is not one of the main species in the solution equilibrium. At pH just below 5.5 the main species present in a 5μM solution of Al Another common instance where precipitation occurs is when a metal cation interacts with an anionic ligand to form an electrically neutral complex. If the complex is hydrophopbic it will precipitate out of water. This occurs with the nickel ion Ni ## Minimization of Gibbs energyAt equilibrium, For a closed system, no particles may enter or leave, although they may combine in various ways. The total number of atoms of each element will remain constant. This means that the minimization above must be subjected to the constraints: where This is a standard problem in optimisation, known as constrained minimisation. The most common method of solving it is using the method of Lagrange multipliers, also known as undetermined multipliers (though other methods may be used). Define: where the λ - and
(For proof see Lagrange multipliers) This is a set of This method of calculating equilibrium chemical concentrations is useful for systems with a large number of different molecules. The use of ## See also- Equilibrium constant
- Determination of equilibrium constants
- Henderson-Hasselbalch equation
- Michaelis-Menten kinetics
- Redox equilibria
- Thermodynamic databases for pure substances
## References**^**Atkins & Jones, 2001**^**Gold Book definition Link**^***Chemistry: Matter and Its Changes*James E. Brady , Fred Senese 4th Ed.__ISBN 0471215171__**^***Chemical Principles: The Quest for Insight*Peter Atkins, Loretta Jones 2nd Ed.__ISBN 0716757010__**^**Physical Chemistry by Atkins, De Paula**^**P.W. Atkins, Physical Chemistry, Oxford University Press, date**^**a) Mary Jane Schultz. Why Equilibrium? Understanding the Role of Entropy of Mixing.*Journal of Chemical Education***1999**,*76*, 1391. b) Clugston, Michael J. A mathematical verification of the second law of thermodynamics from the entropy of mixing.*Journal of Chemical Education***1990**,*67*, 203.**^**C.W. Davies,*Ion Association*,Butterworths, 1962- ^
^{a}^{b}I. Grenthe and H. Wanner,*Guidelines for the extrapolation to zero ionic strength*, http://www.nea.fr/html/dbtdb/guidelines/tdb2.pdf **^**F.J,C. Rossotti and H. Rossotti,*The Determination of Stability Constants*, McGraw-Hill, 1961- ^
^{a}^{b}^{c}*Concise Encyclopedia Chemistry*1994__ISBN 0899254578__ **^**M.T. Beck,*Chemistry of Complex Equilibria*, Van Nostrand, 1970. 2nd. Edition by M.T. Beck and I Nagypál, Akadémiai Kaidó, Budapest, 1990.- ^
^{a}^{b}NASA Reference publication 1311, Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications **^**This approach is described in detail in W. R. Smith and R. W. Missen,*Chemical Reaction Equilibrium Analysis: Theory and Algorithms*, , Krieger Publishing, Malabar, Fla, 1991 (a reprint, with corrections, of the same title by Wiley-Interscience, 1982). A comprehensive treatment of the theory of chemical reaction equilibria and its computation. Details at http://www.mathtrek.com/**^**The diagram was created with the program HySS
## Further reading- F. Van Zeggeren and S.H. Storey,
*The Computation of Chemical Equilibria*, Cambridge University Press, 1970. Mainly concerned with gas-phase equilibria. - D. J. Leggett (editor),
*Computational Methods for the Determination of Formation Constants*, Plenum Press, 1985. - A.E. Martell and R.J. Motekaitis,
*The Determination and Use of Stability Constants*, Wiley-VCH, 1992. - P. Gans,
*Stability Constants: Determination and Uses, an interactive CD,*Protonic Software (Leeds), 2004
## Software for chemical equilibria- Aqua solution software A set of five computer programs for
- Specific Interaction Theory. An editable database of published SIT parameters. Estimation of SIT parameters and adjustment of stability constants for changes in ionic strength.
- Calculation of electrolyte activity coefficients, ionic activity coefficients, osmotic coefficients
- Calculation of acid-base equilibria in electrolyte solutions and sea water
- Calculation of O
_{2}solubility in water, electrolyte solutions, natural fluids and seawater as a function of temperature, concentration, salinity, altitude, external pressure, humidity - Prediction of temperature dependence of lg K values using various thermodynamic models
- JESS:A powerful research tool for thermodynamic and kinetic modelling of chemical speciation in complex aqueous environments.
- Chemical Equilibrium Calculator
Categories: Analytical chemistry | Physical chemistry |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Chemical_equilibrium". A list of authors is available in Wikipedia. |